The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  1  1 12  4  2  1  8  2  4  1  2  8  1  1  1  2  1  1 12  2  0  1  2  8  2  4  1  1  2  2  1  4  1  1  1  1  2  1  2  0  2  1
 0  2  0  2  0  0 14  6  4  2  4 14 12  6 12  2  0  4 12  8  0  6  6  2 14  2 14 10 14  2 14  4  2  8 12  0  2 14  2 12  6  8 10  4 12  4 10 14  2 10  2  6 10  2  6 12 12  0  8 14  8  2  0  8  2  0  0  6  4  4  4 10
 0  0  2  2 12  6 14  0  4  6  2 12  0 10  6 12  8  2  0  2 12  0 12  2 10 14  0  8  6 10 12  6  0  2  2  0  8  8  6  6 14  2  4  2  4  6 14  6  8  4 10  6  4  4  2  2 10 14  2  2  2 10  0  0  6  4 10  6  6  2  6  4
 0  0  0  4  0  0 12  8  8 12  0  0  8  4  0  8  0  0  8  0  0  0  8  0  0  8  4 12  8  4 12 12  8 12 12  4  4  4 12 12  0 12  4 12 12 12  8  4  0  4 12  0 12  0 12  8  0  4 12  8 12  8 12 12  4  4  8  8  4 12 12  4
 0  0  0  0  8  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  8  0  8  8  8  0  8  8  0  8  0  0  8  8  8  0  0  8  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  8  8  8  8  0  0  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  0  8  0  8  8  0  0  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  0  0  0  8  0  0  8  8  0  0  8  8  8  0  0  8  0  0  8  0  0  0  0  8  8

generates a code of length 72 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+164x^63+292x^64+544x^65+808x^66+1318x^67+1580x^68+2680x^69+3111x^70+3954x^71+3896x^72+4310x^73+2984x^74+2466x^75+1735x^76+1228x^77+606x^78+462x^79+204x^80+184x^81+88x^82+80x^83+28x^84+12x^85+19x^86+4x^87+6x^88+2x^89+1x^92+1x^96

The gray image is a code over GF(2) with n=576, k=15 and d=252.
This code was found by Heurico 1.16 in 23.2 seconds.